Bach-flat manifolds and conformally Einstein structures

• Author(s): Ixchel Dzohara Gutiérrez Rodríguez,
• Publisher: Universidade de Santiago de Compostela
• Pages: 196
• ISBN_10: 8489390592
  ISBN_13: 9788489390591
  
• Language: es

Description:... "Einstein manifolds, being critical for the Hilbert-Einstein functional, are central in Riemannian Geometry and Mathematical Physics. A strategy to construct Einstein metrics consists on deforming a given metric by a conformal factor so that the resulting metric is Einstein. In the present Thesis we follow this approach with special emphasis in dimension four. In this work we classify four-dimensional homogeneous conformally Einstein manifolds and provide a large family of strictly Bach-flat gradient Ricci solitons. We show the existence of Bach-flat structures given as deformations of Riemannian extensions by means of the Cauchy-Kovalevskaya theorem."--Publisher